A simple analytical form for yield surface distortion under non-associated flow rule is developed from the expression of the transformed second and third deviatoric stress invariants in Yoon et al. (2014). The developed analytical yield criterion has the same ability as the original yield criterion to describe material's strength differential (SD) effect. Compared with Yoon et al. (2014) criterion, the material parameters in the analytical form presented in this study can be directly calculated from the tension and compression stresses along 0 degrees, 45 degrees, 90 degrees and equi-biaxial directions, which doesn't need any optimization process and interpolation to describe the evolution of asymmetric yield surface under the proportional loadings. The proposed yield criterion can accurately predict the anisotropic hardening along 0 degrees, 45 degrees, 90 degrees and equi-biaxial directions under tension and compression, which will make the significant improvements in the stress predictions including 15 degrees, 30 degrees, 60 degrees and 75 degrees. To guarantee the convexity of yield surface during loading history, the minimum order of principal minor determinant is checked. The proposed yield criterion has been successfully applied for HCP materials to validate its general applicability for describing anisotropy/asymmetry-induced distorted yield surface during deformation. In addition, an analytical asymmetric plastic potential function is developed based on Poly4 yield function. The accuracy of the proposed plastic potential function for r-value evolution under tension and compression has been verified by applying it to different materials.